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A fair, six-sided dice is rolled two times. Let X1 and X2 denote the number of points showing on the ¯rst and second rolls, respectively. Let U = X1+X2 and V = X1¡X2.

(a) Find the mean and variance of V .
(b) Find the covariance of U and V .
(c) What is the probability that X2 < X1?
(d) What is the probability that U = V ?

 

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